1. De Broglie Waves, Uncertainty, and Atoms
Physics 1161: Lecture 22a
De Broglie Waves, Uncertainty, and Atoms
sections 30.5 – 30.7 1

2. Compton Scattering Energy of a photon
This experiment really shows photon momentum!
Pincoming photon + 0 = Poutgoing photon + Pelectron
Electron at rest
Outgoing photon has momentum p and wavelength 
Incoming photon has momentum, p, and wavelength l
Recoil electron carries some momentum and KE
Energy of a photon

3. Photons with equal energy and momentum hit both sides of a metal plate
Photons with equal energy and momentum hit both sides of a metal plate. The photon from the left sticks to the plate, the photon from the right bounces off the plate. What is the direction of the net impulse on the plate?
Left
Right
Zero

4. Photons with equal energy and momentum hit both sides of a metal plate
Photons with equal energy and momentum hit both sides of a metal plate. The photon from the left sticks to the plate, the photon from the right bounces off the plate. What is the direction of the net impulse on the plate?
Left
Right
Zero
Photon that sticks has an impulse p
Photon that bounces has an impulse 2p!

5. De Broglie Waves
So far only for photons have wavelength, but De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…...
Explains why we can see interference and diffraction for material particles like electrons!!

6. Preflight 22.5 Which baseball has the longest De Broglie wavelength?
(1) A fastball (100 mph)
(2) A knuckleball (60 mph)
(3) Neither - only curveballs have a wavelength

7. Preflight 22.5 Which baseball has the longest De Broglie wavelength?
(1) A fastball (100 mph)
(2) A knuckleball (60 mph)
(3) Neither - only curveballs have a wavelength
Lower momentum gives higher wavelength.
p=mv, so slower ball has smaller p.

8. A stone is dropped from the top of a building
A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls?
1. It decreases.
It increases.
It stays the same.

9. A stone is dropped from the top of a building
A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls?
1. It decreases.
It increases.
It stays the same.
Speed, v, and momentum, p=mv, increase.

10. Comparison: Wavelength of Photon vs. Electron
Example
Comparison: Wavelength of Photon vs. Electron
Say you have a photon and an electron, both with 1 eV of energy. Find the de Broglie wavelength of each.
Equations are different - be careful!
Photon with 1 eV energy:
Big difference!
Electron with 1 eV kinetic energy:
Solve for

11. Preflights 22.4, 22.5
Photon A has twice as much momentum as Photon B. Compare their energies.
EA = EB
EA = 2 EB
EA = 4 EB
Electron A has twice as much momentum as Electron B. Compare their energies.
EA = EB
EA = 2 EB
EA = 4 EB

12. Preflights 22.4, 22.5
Photon A has twice as much momentum as Photon B. Compare their energies.
EA = EB
EA = 2 EB
EA = 4 EB
and so
double p then double E
Electron A has twice as much momentum as Electron B. Compare their energies.
EA = EB
EA = 2 EB
EA = 4 EB
double p then quadruple E

13. Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy.
lbowling > lgolf
lbowling = lgolf
3. lbowling < lgolf

14. Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy.
lbowling > lgolf
lbowling = lgolf
3. lbowling < lgolf

15. Heisenberg Uncertainty Principle
Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa.
If we know the momentum p, then we know the wavelength , and that means we’re not sure where along the wave the particle is actually located! l y

16. Preflight 23.7 to be precise...
Of course if we try to locate the position of the particle along the x axis to Dx we will not know its x component of momentum better than Dpx, where
and the same for z.
Preflight 23.7
According to the H.U.P., if we know the x-position of a particle, we can not know its:
(1) Y-position (2) x-momentum
(3) y-momentum (4) Energy
51% correct

17. to be precise... Preflight 23.7
Of course if we try to locate the position of the particle along the x axis to Dx we will not know its x component of momentum better than Dpx, where
and the same for z.
Preflight 23.7
According to the H.U.P., if we know the x-position of a particle, we can not know its:
(1) Y-position (2) x-momentum
(3) y-momentum (4) Energy
51% correct

18. Early Model for Atom Plum Pudding
positive and negative charges uniformly distributed throughout the atom like plums in pudding - +
But how can you look inside an atom m across?
Light (visible) l = 10-7 m
Electron (1 eV) l = 10-9 m
Helium atom l = m

19. Rutherford Scattering
Scattering He++ nuclei (alpha particles) off of gold. Mostly go through, some scattered back!
(Alpha particles = He++)
Only something really small (i.e. nucleus) could scatter the particles back!
Atom is mostly empty space with a small (r = m) positively charged nucleus surrounded by cloud of electrons (r = m)

20. Atom is mostly empty space Size is electronic
Atomic Scale
Kia – Sun Chips Model
Nucleons (protons and neutrons) are like Kia Souls (2000 lb cars)
Electrons are like bags of Sun Chips (1 lb objects)
Sun Chips are orbiting the cars at a distance of a few miles
(Nucleus) BB on the 50 yard line with the electrons at a distance of about 50 yards from the BB
Atom is mostly empty space
Size is electronic

21. Recap Photons carry momentum p=h/l Everything has wavelength l=h/p
Uncertainty Principle DpDx > h/(2p)
Atom
Positive nucleus m
Electrons “orbit” m
Classical E+M doesn’t give stable orbit
Need Quantum Mechanics!